Since it is illegal for non-citizens to vote in federal elections, it is not logical that non-citizens would be able to indirectly influence or skew votes in Congress or in the Electoral College vote for President.
An illegal alien or a legal resident who is following the process and waiting in line to become a U.S. citizen is removed from the process if they register to vote.
“Since enactment of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996, federal law has prohibited noncitizens from voting in federal elections, punishing them by fines, imprisonment, inadmissibility and deportation.”
What part of illegal do you not understand?
The U.S. is a republic, which means like ancient Athens, Greece, the rule of law is the controlling factor, not the rule of mercurial and popularist opinions of people.